{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDE-FIND for the Nonlinear Schrodinger Equation\n",
    "\n",
    "Samuel Rudy, 2016\n",
    "\n",
    "This notebook demonstrates PDE-FIND on the Nonlinear Schrodinger Equation.\n",
    "\n",
    "\\begin{align*}\n",
    "i u_t &+ \\frac{1}{2} u_{xx} + |u|^2 u = 0\\\\\n",
    "u_t &= 0.5 i u_{xx} + i |u|^2u\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (12, 8)\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from PDE_FIND import *\n",
    "import scipy.io as sio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = sio.loadmat('./canonicalPDEs/nls.mat')\n",
    "u = data['usol']\n",
    "x = data['x'][0]\n",
    "t = data['t'][:,0]\n",
    "dt = t[1]-t[0]\n",
    "dx = x[2]-x[1]\n",
    "\n",
    "n = len(x)\n",
    "m = len(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3906124dd0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ARKqXltVaPrXW+vG1cCIazBWYAH8sbER0aSRi+Vz0yhJbT8QWi8Uq/2urFZbn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ajVCr1dLpq1ardfg2/OStQYIgSKOzbqd5y3btpaNxVK6WV9ThtiYqV52mzrSgam28CwgIQFBQ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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f39061720d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, T = np.meshgrid(x, t)\n",
    "fig = figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, T, abs(u), rstride=1, cstride=1, cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False)\n",
    "title(r'Nonlinear Schrodinger Equation: $|u(x,t)|$', fontsize = 20)\n",
    "xlabel('x', fontsize = 16)\n",
    "ylabel('t', fontsize = 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct $\\Theta (U)$ and compute $U_t$\n",
    "\n",
    "Printed out is a list of candidate functions for the PDE.  Each is a column of $\\Theta (U)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ut = np.zeros((m,n), dtype=np.complex64)\n",
    "ux = np.zeros((m,n), dtype=np.complex64)\n",
    "uxx = np.zeros((m,n), dtype=np.complex64)\n",
    "uxxx = np.zeros((m,n), dtype=np.complex64)\n",
    "\n",
    "for i in range(n):\n",
    "    ut[:,i] = FiniteDiff(u[:,i], dt, 1)\n",
    "for i in range(m):\n",
    "    ux[i,:] = FiniteDiff(u[i,:], dx, 1)\n",
    "    uxx[i,:] = FiniteDiff(u[i,:], dx, 2)\n",
    "    uxxx[i,:] = FiniteDiff(u[i,:], dx, 3)\n",
    "    \n",
    "ut = np.reshape(ut, (n*m,1), order='F')\n",
    "ux = np.reshape(ux, (n*m,1), order='F')\n",
    "uxx = np.reshape(uxx, (n*m,1), order='F')\n",
    "uxxx = np.reshape(uxxx, (n*m,1), order='F')\n",
    "X_ders = np.hstack([np.ones((n*m,1)),ux,uxx,uxxx])\n",
    "X_data = np.hstack([np.reshape(u, (n*m,1), order='F'), np.reshape(abs(u), (n*m,1), order='F')])\n",
    "derivatives_description = ['','u_{x}','u_{xx}', 'u_{xxx}']\n",
    "\n",
    "X, rhs_des = build_Theta(X_data, X_ders, derivatives_description, 3, data_description = ['u','|u|'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['',\n",
       " 'u_{x}',\n",
       " 'u_{xx}',\n",
       " 'u_{xxx}',\n",
       " '|u|',\n",
       " 'u|u|^2',\n",
       " 'u^3',\n",
       " '|u|^3',\n",
       " 'u|u|',\n",
       " 'u^2',\n",
       " 'u^2|u|',\n",
       " 'u',\n",
       " '|u|^2',\n",
       " '|u|u_{x}',\n",
       " 'u|u|^2u_{x}',\n",
       " 'u^3u_{x}',\n",
       " '|u|^3u_{x}',\n",
       " 'u|u|u_{x}',\n",
       " 'u^2u_{x}',\n",
       " 'u^2|u|u_{x}',\n",
       " 'uu_{x}',\n",
       " '|u|^2u_{x}',\n",
       " '|u|u_{xx}',\n",
       " 'u|u|^2u_{xx}',\n",
       " 'u^3u_{xx}',\n",
       " '|u|^3u_{xx}',\n",
       " 'u|u|u_{xx}',\n",
       " 'u^2u_{xx}',\n",
       " 'u^2|u|u_{xx}',\n",
       " 'uu_{xx}',\n",
       " '|u|^2u_{xx}',\n",
       " '|u|u_{xxx}',\n",
       " 'u|u|^2u_{xxx}',\n",
       " 'u^3u_{xxx}',\n",
       " '|u|^3u_{xxx}',\n",
       " 'u|u|u_{xxx}',\n",
       " 'u^2u_{xxx}',\n",
       " 'u^2|u|u_{xxx}',\n",
       " 'uu_{xxx}',\n",
       " '|u|^2u_{xxx}']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rhs_des"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve for $\\xi$\n",
    "\n",
    "TrainSTRidge splits the data up into 80% for training and 20% for validation.  It searches over various tolerances in the STRidge algorithm and finds the one with the best performance on the validation set, including an $\\ell^0$ penalty for $\\xi$ in the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDE derived using STRidge\n",
      "u_t = (-0.000000 +0.500310i)u_{xx}\n",
      "    + (-0.000000 +0.999674i)u|u|^2\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "# Solve with STRidge\n",
    "w = TrainSTRidge(X,ut,10**-5,500)\n",
    "print \"PDE derived using STRidge\"\n",
    "print_pde(w, rhs_des)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0473\n",
      "0.0147\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([(1j*(0.5-0.500310))*100/0.5, (1j*(1-0.999674))*100]))\n",
    "print mean(err)\n",
    "print std(err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Same as above but with added noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Now try to do it with noise.\n",
    "numpy.random.seed(0)\n",
    "un = u + 0.01/np.sqrt(2)*std(real(u))*np.random.randn(u.shape[0],u.shape[1]) + 0.01/np.sqrt(2)*1j*std(imag(u))*np.random.randn(u.shape[0],u.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "width_x = 10\n",
    "width_t = 10\n",
    "deg = 4\n",
    "\n",
    "m,n=u.shape\n",
    "\n",
    "m2 = m-2*width_t\n",
    "n2 = n-2*width_x\n",
    "\n",
    "utn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "uxn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "uxxn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "uxxxn = np.zeros((m2,n2), dtype=np.complex64)\n",
    "\n",
    "for i in range(n2):\n",
    "    utn[:,i] = PolyDiff(real(un[:,i+width_x]), dt*np.arange(m), deg = deg, width = width_t)[:,0]\n",
    "    utn[:,i] = utn[:,i]+1j*PolyDiff(imag(un[:,i+width_x]), dt*np.arange(m), deg = deg, width = width_t)[:,0]\n",
    "\n",
    "for i in range(m2):\n",
    "    x_derivatives = PolyDiff(real(un[i+width_t,:]), dx*np.arange(n), deg = deg, diff = 3, width = width_x)\n",
    "    x_derivatives = x_derivatives+1j*PolyDiff(imag(un[i+width_t,:]), dx*np.arange(n), deg = deg, diff = 3, width = width_x)\n",
    "    uxn[i,:] = x_derivatives[:,0]\n",
    "    uxxn[i,:] = x_derivatives[:,1]\n",
    "    uxxxn[i,:] = x_derivatives[:,2]\n",
    "\n",
    "utn = np.reshape(utn, (n2*m2,1), order='F')\n",
    "uxn = np.reshape(uxn, (n2*m2,1), order='F')\n",
    "uxxn = np.reshape(uxxn, (n2*m2,1), order='F')\n",
    "uxxxn = np.reshape(uxxxn, (n2*m2,1), order='F')\n",
    "Xn_ders = np.hstack([np.ones((n2*m2,1)),uxn,uxxn,uxxxn])\n",
    "Xn_data = np.hstack([np.reshape(un[width_t:m-width_t,width_x:n-width_x], (n2*m2,1), order='F'),\n",
    "                     np.reshape(abs(un[width_t:m-width_t,width_x:n-width_x]), (n2*m2,1), order='F')])\n",
    "derivatives_description = ['','u_{x}','u_{xx}', 'u_{xxx}']\n",
    "\n",
    "Xn, rhs_des = build_Theta(Xn_data, Xn_ders, derivatives_description, 3, data_description = ['u','|u|'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDE derived using STRidge\n",
      "u_t = (0.000134 +0.478631i)u_{xx}\n",
      "    + (0.000078 +0.981648i)u|u|^2\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "# Solve with STRidge\n",
    "lam = 10**-5\n",
    "d_tol = 500\n",
    "\n",
    "wn = TrainSTRidge(Xn,utn,lam,d_tol)\n",
    "print \"PDE derived using STRidge\"\n",
    "print_pde(wn, rhs_des)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.05455030161\n",
      "1.21933372583\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([(1j*(0.5-0.478631)+0.000134)*100/0.5, (1j*(1-0.981648)+0.000078)*100]))\n",
    "print mean(err)\n",
    "print std(err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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